Finite Group Databasebeta

← #14908324

Subgroups — #14908324

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13078271C211yesmaximal, characteristic, complemented
4#13070727C212yesmaximal, complemented
5#13070722C212yesmaximal, complemented
6#13070710C212yesmaximal, complemented
7#13070705C212yesmaximal, complemented
8#13070402C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10C2×#10622130C211yesmaximal, characteristic, complemented
11C11×#3061C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#537—21no—
15#10623356—21no—
16C22×Dic44C2211yescharacteristic
17C11×#468—22no—
18C11×#467C2212yes—
19C11×#466C2212yes—
20C2×C11×#107C2211yescharacteristic
21C11×#417—21no—
22#10622808—24no—
23C2×#66893C2212yes—
24C2×#66891C2212yes—
25#10622753—24no—
26#10622750—22no—
27#10622733—21no—
28#10622729C2212yes—
29#10622729C2212yes—
30#10622719C2211yescharacteristic
31C2×#66876C2212yes—
32C2×#66876C2211yescharacteristic
33C22×C11⋊C16C2212yes—
34C22×C11⋊C16C2211yescharacteristic
35#10622202C2211yescharacteristic
36#10622202C2211yescharacteristic
37#10622200C2211yescharacteristic
38#10622200C2211yescharacteristic
39#10622130C2212yes—
40#10622130C2212yes—
41#10622128C2212yes—
42#10622127C2212yes—
43C2×C11×#41—21no—
44C2×C11×#41D411yescharacteristic
45C22×Dic22—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C11×#131—22no—
52C11×#131—22no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D412yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—41no—
59C11×#121—22no—
60C11×#121—41no—
61C11×#121—42no—
62C2×C11×C4⋊C4—21no—
63#66997—41no—
64#66989—41no—
65#66988—42no—
66#66979—21no—
67#66977—22no—
68#66977—22no—
69C2×Dic44—22no—
70C2×Dic44—22no—
71C2×Dic44—21no—
72C2×Dic44C2312yes—
73C11×#107—21no—
74C11×#107C2312yes—
75C11×#103—22no—
76C11×#102—22no—
77#66893—24no—
78#66891—24no—
79#66882C2311yescharacteristic
80#66882C2311yescharacteristic
81#66881—21no—
82#66880—22no—
83#66880—22no—
84#66876—24no—
85#66876D414yescomplemented
86C2×C11⋊C16—22no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2311yescharacteristic
89C2×C11⋊C16C2311yescharacteristic
90C2×C11⋊C16C2312yes—
91#33613—111nomaximal, Sylow
92C11×#41—22no—
93C11×#41—22no—
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×Q8×C11D811yescharacteristic
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C2×D4×C11D812yes—
102C2×D4×C11D811yescharacteristic
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×Dic11—41no—
108C2×Dic22—22no—
109C2×Dic22—42no—
110C2×Dic22—41no—
111C2×Dic22—42no—
112C11×Q16—21no—
113C11×Q16—21no—
114C11×SD16—42no—
115C11×D8—21no—
116C11×D8—21no—
117C11×M16—24no—
118C11×M16—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D412yes—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4112yes—
125C2×C8×C11C2411yescharacteristic
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138C4×Dic11—41no—
139Dic44—22no—
140Dic44—22no—
141Dic44—42no—
142C11⋊C16—21no—
143C11⋊C16—21no—
144C11⋊C16C2×D414yes—
145C2×#510—111no—
146C2×#504—111no—
147#3061D1111yescharacteristic
148#3059—111no—
149#2220—112no—
150#2219—112no—
151#2217—112no—
152#2216—112no—
153#2159—111no—
154#2138—111no—
155C2×#358—111no—
156C23×C11—41no—
157C23×C11C2×D812yes—
158C23×C11C2×D811yescharacteristic
159Q8×C11—22no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—24no—
163D4×C11—22no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—82no—
167D4×C11—162no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11—161no—
174C2×C4×C11#12112yes—
175C2×C4×C11C2×D812yes—
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11#13512yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—82no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186C8×C11—22no—
187C8×C11#12112yes—
188C8×C11C22×D411yescharacteristic
189C8×C11C2×#4111yescharacteristic
190C2×#135C2×D1111yescharacteristic
191C22×Q16—111no—
192C2×#131C2×D1111yescharacteristic
193#537—21no—
194#536—221no—
195#510—224no—
196C2×Q32—112no—
197C2×SD32—112no—
198#504—224no—
199C2×M32—111no—
200C2×M32—112no—
201C22×C16—111no—
202C22×C16—112no—
203#470—222no—
204#468—22no—
205#467—112no—
206#467—112no—
207#467C2×D1112yes—
208#466C2×D1112yes—
209#427—111no—
210C2×#107C2×D1111yescharacteristic
211#419—221no—
212#417—21no—
213#367—112no—
214#366—112no—
215#358—111no—
216#358—111no—
217#358—112no—
218#358—112no—
219#357—111no—
220#357—111no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11#46612yes—
230C22×C11C22×D811yescharacteristic
231C4×C11—22no—
232C4×C11—82no—
233C4×C11—81no—
234C4×C11#46612yes—
235C4×C11C2×#12111yescharacteristic
236C4×C11C2×#13511yescharacteristic
237Dic11—81no—
238Dic11—81no—
239Dic11—82no—
240C2×#41—21no—
241C2×#41C22⋊D1111yescharacteristic
242C22×Q8—221no—
243#135—22no—
244#135—22no—
245C2×Q16—112no—
246C2×Q16—222no—
247C2×Q16—222no—
248C2×Q16—221no—
249C2×Q16C22×D1111yescharacteristic
250C2×SD16—21no—
251C2×D8C22×D1111yescharacteristic
252#131—22no—
253#131—22no—
254C2×M16C22⋊D1111yescharacteristic
255C2×M16C22⋊D1112yes—
256C22×C8C22×D1112yes—
257C22×C8C22×D1111yescharacteristic
258C4⋊Q8—441no—
259#124—441no—
260#123—442no—
261C22⋊Q8—22no—
262C22⋊Q8—41no—
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265#121—22no—
266#121—41no—
267#121—42no—
268#117—221no—
269C2×C4⋊C4—21no—
270Q32—224no—
271SD32—224no—
272M32—114no—
273M32—224no—
274C2×C16—112no—
275C2×C16—111no—
276C2×C16—111no—
277C2×C16—224no—
278C2×C16—222no—
279#107—21no—
280#107—111no—
281#107—111no—
282#107C22×D1112yes—
283#106—221no—
284#103—22no—
285#103—222no—
286#103—222no—
287#102—22no—
288C2×C11—22no—
289C2×C11—42no—
290C2×C11—161no—
291C2×C11C2×#46611yescharacteristic
292C2×C11#341611yescharacteristic
293C2×C11#341711yescharacteristic
294#41—22no—
295#41—22no—
296#41—42no—
297#41—42no—
298C2×Q8—21no—
299C2×Q8—222no—
300C2×Q8—441no—
301C2×Q8—442no—
302C2×Q8—442no—
303C2×Q8#432311yescharacteristic
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4#432312yes—
308C2×D4#432311yescharacteristic
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—441no—
312C22×C4C2×C22⋊D1112yes—
313C22×C4C2×C22⋊D1111yescharacteristic
314Q16—21no—
315Q16—21no—
316Q16—222no—
317Q16—222no—
318Q16—442no—
319SD16—42no—
320D8—21no—
321D8—21no—
322M16—22no—
323M16—24no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8D4×D1112yes—
327C2×C8#434112yes—
328C2×C8C2×C22⋊D1112yes—
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—441no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C42—441no—
344C16—114no—
345C16—221no—
346C16—221no—
347C11#3361311yescharacteristic, complemented, Sylow
348C23—41no—
349C23C2×#432312yes—
350C23C2×#432311yescharacteristic
351Q8—22no—
352Q8—41no—
353Q8—41no—
354Q8—442no—
355Q8—442no—
356Q8—882no—
357D4—24no—
358D4—22no—
359D4—41no—
360D4—41no—
361D4—82no—
362D4—162no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—161no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—882no—
373C2×C4C2×#432312yes—
374C2×C4C2×#432311yescharacteristic
375C2×C4#6699212yes—
376C2×C4#6700312yes—
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—22no—
379C8#6699212yes—
380C8C2×D4×D1111yescharacteristic
381C8C2×#434111yescharacteristic
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22#1062265112yes—
391C22C22×#432311yescharacteristic
392C4—22no—
393C4—82no—
394C4—81no—
395C4—881no—
396C4—882no—
397C4—881no—
398C4#1062265112yes—
399C4C2×#6699211yescharacteristic
400C4C2×#6700311yescharacteristic
401C2—22no—
402C2—42no—
403C2—161no—
404C2C2×#1062265111yescharacteristic
405C2#1308176311yescharacteristic
406C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33613
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. C2×#10622753C2semidirect
3. #13078271C2semidirect
4. #13070727C2semidirect
5. #13070722C2semidirect
6. #13070710C2semidirect
7. #13070705C2semidirect
8. #13070402C2semidirect
9. #13070323C2semidirect
10. C2×#10622130C2semidirect
85. #66876D4semidirect
347. C11#33613semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106228082
C2×#106227532
#130782712
#130707272
#130707222
#130707102
#130707052
#130704022
#130703232
C2×#106221302
C11×#30612
#3361311